Eur. Phys. J. B 6, 363-372 (1998)
https://doi.org/10.1007/s100510050562

Reaction kinetics in polymer melts

¹ Department of Chemical Engineering, Columbia University, 500 West 120th Street, New York, NY 10027, USA
² Department of Physics, Columbia University, 538 West 120th Street, New York, NY 10027, USA

Corresponding authors: ^a bo8@columbia.edu - ^b dvav@phys.columbia.edu

Received: 2 June 1998
Revised: 9 July 1998
Accepted: 10 July 1998
Published online: 15 December 1998

Abstract

We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the 2nd order rate constant k after postulating simple physical bounds. Our results generalize previous 2-chain treatments (valid in dilute reactants limit) by Doi [CITE], de Gennes [CITE], and Friedman and O'Shaughnessy [CITE], to arbitrary initial reactive group density n₀ and local chemical reactivity Q. Simple mean field (MF) kinetics apply at short times, . For high Q, a transition occurs to diffusion-controlled (DC) kinetics with (where x_t is rms monomer displacement in time t) leading to a density decay . If n₀ exceeds the chain overlap threshold, this behavior is followed by a regime where during which k has the same power law dependence in time, , but possibly different numerical coefficient. For unentangled melts this gives while for entangled cases one or more of the successive regimes , and may be realized depending on the magnitudes of Q and n₀. Kinetics at times longer than the longest polymer relaxation time τ are always MF. If a DC regime has developed before τ then the long time rate constant is where R is the coil radius. We propose measuring the above kinetics in a model experiment where radical end groups are generated by photolysis.